Global sensitivity analysis of statistical models by double randomization method

The paper addresses a global sensitivity analysis of complex models. The work presents a generalization of the hierarchical statistical models where uncertain parameters determine the distribution of statistical models. The double randomization method is applied to increase the efficiency of the Monte Carlo estimation of Sobol indices. Numerical computations are provided to study the accuracy and efficiency of the proposed technique. The issue of optimization of the suggested approach is considered.

Monte carlo estimation of the solution of fractional partial differential equations

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of errors between the exact solution and the Monte Carlo approximation, the estimate of the fluctuation via the appropriate central limit theorem (CLT) and the construction of confidence intervals. Moreover, we provide rates of convergence in the CLT via Berry-Esseen type bounds. Concrete numerical computations and illustrations are included.

Monte Carlo estimation of the probability of causal contacts between communicating civilizations

In this work we address the problem of estimating the probabilities of causal contacts between civilizations in the Galaxy. We make no assumptions regarding the origin and evolution of intelligent life. We simply assume a network of causally connected nodes. These nodes refer somehow to intelligent agents with the capacity of receiving and emitting electromagnetic signals. Here we present a three-parametric statistical Monte Carlo model of the network in a simplified sketch of the Galaxy. Our goal, using Monte Carlo simulations, is to explore the parameter space and analyse the probabilities of causal contacts. We find that the odds to make a contact over decades of monitoring are low for most models, except for those of a galaxy densely populated with long-standing civilizations. We also find that the probability of causal contacts increases with the lifetime of civilizations more significantly than with the number of active civilizations. We show that the maximum probability of making a contact occurs when a civilization discovers the required communication technology.